What is (\partial)/(\partial y)(sqrt(2+x^2+y^2)) ?

The answer to (\partial)/(\partial y)(sqrt(2+x^2+y^2)) is y/(sqrt(2+x^2+y^2))

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(\partial)/(\partial y)(sqrt(2+x^2+y^2))

\frac{\partial}{\partial y} (2 + x^{2} + y^{2})

\frac{y}{2 + x ^{2} + y ^{2}}

Solution steps

\frac{\partial}{\partial y} (2 + x^{2} + y^{2})

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 2 + x ^{2} + y ^{2}} \frac{\partial}{\partial y} (2 + x^{2} + y^{2})

= \frac{1}{2 2 + x ^{2} + y ^{2}} \frac{\partial}{\partial y} (2 + x^{2} + y^{2})

\frac{\partial}{\partial y} (2 + x^{2} + y^{2}) = 2 y

= \frac{1}{2 2 + x ^{2} + y ^{2}} \cdot 2 y

Simplify

\frac{1}{2 2 + x ^{2} + y ^{2}} \cdot 2 y : \frac{y}{2 + x ^{2} + y ^{2}}

= \frac{y}{2 + x ^{2} + y ^{2}}

x sin (- 2 x), at π

x \to 0 lim (\frac{x}{x ^{2} + 6 x})

\int t + 8 d t

\int x^{3} + x^{2} d x

\frac{d}{d x} (4 - x^{2} + y^{2})

What is (\partial)/(\partial y)(sqrt(2+x^2+y^2)) ?
The answer to (\partial)/(\partial y)(sqrt(2+x^2+y^2)) is y/(sqrt(2+x^2+y^2))